Classical long-distance communication methods are based on the emission and detection of electromagnetic fields (EM fields). Typically, current methods are based upon the modulation of the amplitude, phase, and frequency of these fields. Because EM fields are composed of photons, these fields have additional characteristics that have not been exploited to communicate. One of these characteristics is the spatial and time correlations that exist between photons because of their quantum-mechanical nature.
For many years, the spatial correlations between photons have been exploited in science and technology through the use of a technique called intensity interferometry; for example, to measure stellar angular diameters; to investigate nuclear collisions; to measure electron temperature fluctuations in fusion plasmas; and head-disk spacing in hard drives; to characterize hard synchrotron radiation; as a diagnostic tool in Biology and Chemistry; and recently to investigate the quantum state of Bose-Einstein condensates. In short, up to now, non-local spatial correlations between photons have been used through intensity interferometry as a measurement technique.
FIG. 1 is a diagram 100 demonstrating intensity interferometry, in accordance with an exemplary embodiment of the invention. In FIG. 1, there are two distant random point sources of electromagnetic radiation, i.e., transmitters a 115 and b 120, and there are two independent detectors, i.e., receivers 1 125 and 2 130, at a distance, DR, from each other. The distance between the transmitters and receivers is L. The wavy lines represent different propagation paths for the emitted photons. The detectors need not be directly connected (all field intensity calculations between the two detectors can be done remotely).
Assume that the transmitter sources 115 and 120 are separated in space by DS, the two receivers 125 and 130 by DR, and that the distance from the transmitter sources to the receivers, L, is much larger than DS and DR. Without loss of generality, assume that the radiation pattern is isotropic, and write explicitly the time dependence of the electric field radiated by each antenna, Eα, thusEα=Aα exp(−iωαt+iφα(t)),  (1)where the subscript identifies the transmitter antenna (α=a,b) and Aα is the amplitude.
On the receiving end, the second order correlation function is defined by
                    C        ⁢                  =          Δ                ⁢                              〈                                          I                1                            ⁢                              I                2                                      〉                                              〈                              I                1                            〉                        ⁢                          〈                              I                2                            〉                                                          (        2        )            where Ij is the EM field intensity at receiver j, Ij=EjE*j (the asterisk denotes complex conjugation) and Ej is the total electric field at detector j from both sources. The sharp brackets indicate a time average over time interval T0. To simplify the discussion, assume that the emission from both sources is at the same frequency ωa=ωb=ω and that both sources emit radiation with the same amplitude, Aa=Ab=A. Furthermore, assume that φa(t) and φb(t) are statistically independent random variables. Then calculate the time averages over a time T0 much larger than the coherence time TC of the sources, i.e., the time over which φα(t) is constant, then the factors that depend on
                              δ          ⁡                      (            t            )                          ⁢                  =          Δ                ⁢                                            Φ              a                        ⁡                          (              t              )                                -                                    Φ              b                        ⁡                          (              t              )                                                          (        3        )            become vanishingly small and may be ignored. Thus, in the far-field region, i.e., DS, DR<<L, and with the above assumptions, the second-order correlation function in eq. (2) is given byC≈1+cos2(Δ)  (4)where λ is the radiation's wavelength and
                    Δ        ⁢                  =          Δ                ⁢                              π            ⁢                                                  ⁢                          D              S                        ⁢                          D              R                                            L            ⁢                                                  ⁢            λ                                              (        5        )            One of ordinary skill in the art will recognize that equation (4) is the basis of Hanbury Brown and Twiss interferometry. One of ordinary skill in the art will understand that the term “Hanbury Brown and Twiss interferometry” is most widely used in astronomy. Accordingly, herein the term “intensity interferometry” will be used. The basis of intensity interferometry is that the linear size of the source, DS, is fixed but unknown, and the experimenter varies the distance between the receivers DR, records the intensities, and calculates the second-order spatial correlation. It is possible to find the angular size θS=DS/L of the source by plotting as a function of DR the reduced second-order correlation, γ,
                    γ        ⁢                  =          Δ                ⁢                              C            -            1                                              C              ⁡                              (                0                )                                      -            1                                              (        6        )            where C(0) is the value of C extrapolated to DR=0. Using equation (4) one can obtainγ=cos2(Δ).  (7)The value of DR where γ first vanishes corresponds to the angular size of the source, θS.
One of ordinary skill in the art will recognize that this is the method that Hanbury Brown and Twiss used to measure the angular size of stellar sources both at radio and optical wavelengths. In their scenario, T0>>TC because the stellar radiation is incoherent on time scales much smaller than the integration time necessary to achieve a good signal to noise ratio.
In the prior art, intensity interferometry has been used to measure the angular size of the source θS=DS/L by varying the distance between receivers DR. Note that according to equation (4) the second-order correlation C is unchanged upon permutation of DS and DR.
Accordingly, there remains a need to exploit the symmetry in intensity interferometry to create a communication channel to transmit information wirelessly.